Uniform Estimate of the Relative Free Energy by the Dissipation Rate for Finite Volume Discretized Reaction-Diffusion Systems

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 77)

Abstract

We prove a uniform Poincaré-like estimate of the relative free energy by the dissipation rate for implicit Euler, finite volume discretized reaction-diffusion systems. This result is proven indirectly and ensures the exponential decay of the relative free energy with a unified decay rate for admissible finite volume meshes.

Keywords

Admissible finite volume mesh reaction-diffusion system free energy discrete Poincaré and Sobolev-Poincaré inequality 

Notes

Acknowledgments

The work was partially supported by the European Commission within the 7th Framework Programme MD\(^3\) “Material Development for Double Exposure and Double Patterning” and by the DFG Research Center Matheon Mathematics for Key Technologies within project D22 “Modeling of Electronic Properties of Interfaces in Solar Cells”.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Physikalisch-Technische BundesanstaltBerlinGermany
  2. 2.Weierstrass InstituteBerlinGermany

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